Approximation to Object Conditional Validity with Inductive Conformal Predictors

TL;DR

This paper introduces an algorithm that approximates object conditional validity in conformal predictors, addressing the challenge of achieving true conditional validity in finite samples by iteratively adjusting conformity measures.

Contribution

A novel algorithm is proposed to approximate object conditional validity in conformal prediction, supported by theoretical analysis and experimental validation.

Findings

Conditional validity is often unachievable in finite samples.

The proposed algorithm effectively improves conditional validity in real datasets.

Experimental results show measurable benefits of the method in practical tasks.

Abstract

Conformal predictors are machine learning algorithms that output prediction sets that have a guarantee of marginal validity for finite samples with minimal distributional assumptions. This is a property that makes conformal predictors useful for machine learning tasks where we require reliable predictions. It would also be desirable to achieve conditional validity in the same setting, in the sense that validity of the prediction intervals remains valid regardless of conditioning on any particular property of the object of the prediction. Unfortunately, it has been shown that such conditional validity is impossible to guarantee for non-trivial prediction problems for finite samples. In this article, instead of trying to achieve a strong conditional validity result, the weaker goal of achieving an approximation to conditional validity is considered. A new algorithm is introduced to do this by iteratively adjusting a conformity measure to deviations from object conditional validity measured in the training data. Along with some theoretical results, experimental results are provided for three data sets that demonstrate (1) in real world machine learning tasks, lack of conditional validity is a measurable problem and (2) that the proposed algorithm is effective at alleviating this problem.